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On the length and number of served customers of the busy period of a generalised M/G/1 queue with finite waiting room
Published online by Cambridge University Press: 01 July 2016
Abstract
Customers arrive in groups to a single server queue with finite waiting room. Two-dimensional distributions for times and numbers of served customers between occurrences of states in the embedded Markov chain are obtained by linear algebra giving systems of equations for joint Laplace-Stieltjes transforms. For M/M/1 a simple recursion relation for the joint transform of the two variables in the title is derived and used to obtained the first and second moments.
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- Copyright © Applied Probability Trust 1973
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